Calculate factors of a number, their sum and see which of the factors are prime

- Type:

The type of the number`..`

- Factors:

The factors for the input`..`

- Sum of Factors:

The sum of all the factors`..`

- Prime Factors:

The prime factors for the input`..`

- Prime Factorization:

The prime factorization for the input`..`

Factors of a number are the list of all integral numbers that can divide it evenly without leaving any remainders. For example, consider the number 16. The factors of 16 are:

`1, 2, 4, 8, 16`

16 is completely divisible by these numbers.

- 16 ÷ 1 = 10
- 16 ÷ 2 = 8
- 16 ÷ 4 = 4
- 16 ÷ 8 = 2
- 16 ÷ 16 = 1

#### Example Factors

Number | Factors |
---|---|

3 | 1, 3 |

10 | 1, 2, 5, 10 |

20 | 1, 2, 4, 5, 10, 20 |

All integers have at least two factors, the number 1 and itself. A number that has only two factors is only divisible by itself and 1. These numbers are called prime numbers. Conversely, all numbers with more than two factors are composite numbers.

## Factor Pairs

Factor pairs are the combination of two factors that give the original number when multiplied together. For example, 16 has the following factor pairs:

Factor Pair | Reason |
---|---|

(1, 16) | 1 × 16 = 16 |

(2, 8) | 2 × 8 = 16 |

(4, 4) | 4 × 4 = 16 |

### How to perform factorization

You find out factors of a number by using a trial division. Let's say our number is **n**.

**Step 1:**Find the**square root**of n and round it down to the nearest whole number. Let's call this number**r**. This square root helps us reduce the calculation.**Step 2:**Begin the trial division with the number 1. All numbers are completely divisible by 1. So, 1 is one of the factors by default. Add the pair (1, n) to our factor pair list.**Step 3:**Repeat the above process for 2 and see if n is entirely divisible by it. If a remainder is left, we skip the number. Otherwise, we build our factor pair by dividing n by 2 and adding it to our factor pair. We repeat this step for all numbers until we reach the square root we obtained in Step 1.**Step 4:**At this point, we have the complete factor list. Perform a union on all the numbers in the factor list. The resultant set of numbers are the factors of our original number n.

#### Example Factorization

Consider the number 20.

**Step 1:**The**square root**of 20 is 4.47. Rounding it down gives us 4.**Step 2:**20 is completely divisible by 1. We add (1, 20) to our factor pair list.**Step 3:**20 is completely divisible by 2. We add (2, 10) to our factor pair list.**Step 4:**20 is not wholly divisible by 3 as we we get a remainder of 2. So, we skip it.**Step 5:**20 is completely divisible by 4. We add (4, 5) to our factor pair list.**Step 6:**We have reached our square root 4 and don't need to iterate any longer. Our factor pairs are:- (1, 20)
- (2, 10)
- (4, 5)

**Step 7:**Performing a union on all the numbers in the factor pairs gives us:`1, 2, 4, 5, 10, 20`

. This list contains all the Factors for the number 20.

#### Other Variations

###### History

- Oct 18, 2021
- Tool Launched

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